Are communities as strong as we think?

Many complex systems, from World Wide Web and online social networks to mobile networks, exhibit community structure in which nodes can be grouped into densely interconnected communities. This special structure has been exploited extensively to design better solutions for many operations and applications such as routing in wireless networks, worm containment and interest prediction in social networks. The outcome of these solutions are sensitive to the network structures, which raises an important question: can communities be broken easily in a network? To answer this question, we introduce a density-based problem formulation for analyzing the vulnerability of communities. Our approach includes the NP-completeness and a O(log k) approximation algorithm for solving the problem where k is the number of communities to be broken. Additionally, we analyze the vulnerability of communities in the context of arbitrary community detection algorithms. The empirical results show that communities are vulnerable to edge removal and in some cases the removal of a small fraction of edges can break the community structure.

[1]  Ying Fan,et al.  Identifying and Characterizing Nodes Important to Community Structure Using the Spectrum of the Graph , 2011, PloS one.

[2]  Nam P. Nguyen,et al.  On the Discovery of Critical Links and Nodes for Assessing Network Vulnerability , 2013, IEEE/ACM Transactions on Networking.

[3]  Shivi Shukla.  Multicasting in Delay Tolerant Networks , 2015 .

[4]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[5]  Robin Palotai,et al.  Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics , 2009, PloS one.

[6]  Pan Hui,et al.  BUBBLE Rap: Social-Based Forwarding in Delay-Tolerant Networks , 2008, IEEE Transactions on Mobile Computing.

[7]  Stephen P. Borgatti,et al.  Identifying sets of key players in a social network , 2006, Comput. Math. Organ. Theory.

[8]  Santo Fortunato,et al.  Finding Statistically Significant Communities in Networks , 2010, PloS one.

[9]  Réka Albert,et al.  Structural vulnerability of the North American power grid. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Claudio Castellano,et al.  Community Structure in Graphs , 2007, Encyclopedia of Complexity and Systems Science.

[11]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[12]  Alan T. Murray,et al.  Modeling s-t path availability to support disaster vulnerability assessment of network infrastructure , 2010, Comput. Oper. Res..

[13]  Qinghua Li,et al.  Multicasting in delay tolerant networks: a social network perspective , 2009, MobiHoc '09.

[14]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[15]  George Karypis,et al.  Multilevel k-way Partitioning Scheme for Irregular Graphs , 1998, J. Parallel Distributed Comput..

[16]  Krishna P. Gummadi,et al.  An analysis of social network-based Sybil defenses , 2010, SIGCOMM 2010.

[17]  Gregory Dobson,et al.  Worst-Case Analysis of Greedy Heuristics for Integer Programming with Nonnegative Data , 1982, Math. Oper. Res..

[18]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[19]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[20]  Panos M. Pardalos,et al.  On New Approaches of Assessing Network Vulnerability: Hardness and Approximation , 2012, IEEE/ACM Transactions on Networking.

[21]  Yanlei Wu,et al.  2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2014, Beijing, China, August 17-20, 2014 , 2014, ASONAM.

[22]  Nam P. Nguyen,et al.  Assessing network vulnerability in a community structure point of view , 2013, 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2013).

[23]  Vipin Kumar,et al.  Parallel Multilevel series k-Way Partitioning Scheme for Irregular Graphs , 1999, SIAM Rev..

[24]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[25]  P. Tan,et al.  Node roles and community structure in networks , 2007, WebKDD/SNA-KDD '07.